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Solved Problems-3

Problems-3
A sinusoidal voltage 25 sin 10t is applied at time t = 0 to a circuit as shown in the figure. Find the current i(t), by Laplace transform method. R = 5Ω and L = 1H.
 
Description: Description: Description: 1120.png
 
Solution
By KVL, Description: Description: 7173.png
 
with zero initial condition.
I(s) = Description: Description: 7179.png
 
Description: Description: 7192.png
 
A1 = Description: Description: 7198.png
 
where, A2 = Description: Description: 7204.png
A3 = Description: Description: 7210.png
 
Substituting these,
I(s) = Description: Description: 7216.png
 
Taking inverse Laplace transform,
 
i(t) = Description: Description: 7227.png
Description: Description: 7233.png
Description: Description: 7239.png
Description: Description: 7251.png
or i(t) = Description: Description: 7257.png
 




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